Vector calculating machine



A. H. KENT VECTOR CALCULATING MACHINE Dec. 5, 1944.

Filed- Dec. 11, 1942 2 Sheets-Sheet l INVENTOR ALLEN H. KENT Dec. 5,1944. A. H. KENT VECTOR CALCULATING MACHINE Filed Dec. 11, 1942 2sheets-fsheet =2 INVENTOR ALLEN H. KENT ATTORNEY IIIIIIILI Patented Dec.5, 1944 UNITED "STAT ES PAH-TENT OFF-ICE .rAllen fl. Kent, New York,N..LY,.,.:assig-norl.to Valid,

Ind, Pasadena, .(lalif.,-a corporation or .Cali- *forniamAppllcationDecemberi 11, 1942,i Serial'No.-=468;640

2'Claims.

This invention relates 'to a vector calculating machine and moreparticularlyto' a machine for computingthatrue course and speed of *acraft such' as an airplane or ship which -mVes in a fluid medium. "Tosimplify the description of the machineit w'ill' behereinafter'describedwith reference only to airplanes, it beingunderstood that thesamemachine, without any structural alterations, "but merely "a changeofscales, can be -employed tdsolve ship navigation problems. It is wellknown that the groundspeed of-an airplane (hereinafter referred to 'asground speed) *is-not'the same-as theair speed 'of=-an airplane(hereinafter referred to as air speed"), butisafiected 'by the directionand speed of the wind. 'Heretofore; the influence of the wind upon theground speed and the "ground headingof the airplanedhereinafterreferredtoas the track) has 'beentrigonometrically calculated or hasbeen determinedfby plotting vectors 'on a sheet of paper;

The 'tri'gonometrical "calculation had'the disadvantage "of requiring('a) special skill andtrainingon-the'part ofpthe-computer, ('11)reference to'exten'ded trigonometrical tables, (0) the :use of "arelatively complicated formula 1 and d) lengthycalcu'lations. 'The'papervector-plotting method, "on "the other hand, was neither rapid norpractical. f

It" is the object of; the present inventiorrto pro vide avectorcalcuiatin-g'me'chanism which will compute the effect of thewind'uponthe ground speed with'great accuracy,=simplicity-and"rapiditypa'nd in whose use an operator'may be easilytrained.

A further' object of the invention'isto provide a machine of thecharacter "described 'which is adapte'dtobeusedin conjunction with*a'map fixed on a plottingboard; which "can be readily orientatedrelative thereto, and which "can *be employed as a draftingdnstrumenttolayoutor be placed 1 in coincidence with a 'line on the maprepresenting the track.

A further obj ect' of the" invention isto-provide a machine of the 7character -described in "which all'the factors;-such"as for example,wind, speed, wind direction, ground speed, track; air speed, andairheading of the "airplane '(h'ereinafterreferred to as air heading dcanbe independ-ently set, and which is so constructed that when oneor-more of these factors" are changed, it isnot necessary to disturb thesetting of the ='factors which it is desired to 'hold constant.

An additional "object-of the invent-ion 'isto provide "a "machine -of"the "character described obvious ezmd inypart hereinafterx pointed:out.

The]. invention accordingly :consists, in, features -of 'constmction,combinations of elements and.

arrangementcof rparts which will be exemplified insthewonstructionshereinafter described and of rwhzichzt he :scope of a-application willbeindicatedrintthercla-ims.

4 In Jtheeaccompanyingadrawings;. in i which are shown vvarious:possible embodiments: of this: invention,

JFig, =,1:-.;is 11313131811 view of a machine. embodying my:inventionrusedvwith a. map;

iFigs.:2,l3,-4;-' and 5: are: enlarged :detail sectional views takenalongt'the lines :2.- 2, 33,-- 4-.-l: and 5-5 :respectively of "Fig. 1;

Fig.;;61 is a sectional' view-takensa1ong the line G-afi. ofiE-ig. :4;

Fig. isea: bottom-'- view of the: machinepand1Fig.::8:.is:;az..detail"viewisimilar to Fig. -.4 .of a machine-1embodying ta Imodified form of the invention.

Referring IIOWitOithB 'drawingscand more particrilarlyttorfigs.:11t-hrough Fig. 7, I have there shown x-a machine t0=-embodying myinvention. said' machine is particularly adapted to beused onaplottingzboardalz onswhicha map covering the route to: be flown islain. "ZThe machine 4 l 0 essentially includes: a parallelmotion-'system fli: of. any time well knownrto the art and a computinghead l8 especially 'constructed. in accordance r with: my invention.

Theparallel motion system 'caninclude a conventionalanchor (not :shown)which may bein the form -of -a (Z-clamp whichfirmly :grasps theplottingboar d 1 l2. Rotatably mounted on the C-clamp is alevertnotshown) which turns-about the-center of apulleyn (not shown) fixedon-.the clamp. 'The'other 'end .of the lever carries a second! lever' 20tand a pair' of commonly rotatable pulleys (notshown). One ofthesepulleys is connected' to i thei'flxedrpulley by .a taut band (notshown). -Theireeend of the leverin rigidly supports a flttin'g 22 whichrotatably r carries. a pulley 24 on a ball-bearing:journal '26. A tape28is stretched over-the pulley 24 on one end of the lever 20 =andoverthe second of the pair of commonly-rotatable pulleys. As is well knownin' the art, -"the parallel motion "system just described is such-thatwhen the pulley'u is moved aroundrthe board, .zaline therethrough willbe moved parallel to "itself. "Inother words, when curate. that is,as'its head is moved around the board it will vary from parallelism tolesser degree than does the head in the band-type sys-.

tern. However, the band-type system requires less room for operationsince the head of a bandtype system can be moved along the edge of theboard to which the C-clampis attached without having the levers extendbeyond the board. In the rod-type system it is necessary to allow thelevers to project beyond the board in certain positions of the head.This latter drawback is a serious disadvantage when the calculatingmachine is used in airplanes where space is very limited.

The computing head I8 includes a protractor dial 30 having azimuthgraduations 32 imprinted around its periphery. Said dial is rotatablymounted on' the head in order that the zero azimuth graduation may beset to parallel north hearing on the map I4 and means is provided to fixthe dial in this position so that as the head is moved over the map thezero point will continue to bear true north. To this end the protractordial is centrally apertured and rotatably received on the reduced end ofa bushin 34 (Figs. 2 and 3) fixed to a sleeve 36 force-fitted within theinner race 38 of the ball-bearing journal 26 for the pulley 24. Thelower end of the sleeve 36 has a flange 40 extending therefrom andunderlying the bottom face of the protractor dial 30 to prevent the dialfrom shifting axially of the bushing 34. A ring 42 of L-shapedcross-section is rigidly secured to the protractor dial 30, said ringand dial being concentrically arranged. The flange 44 of said ring liesbetween an ear 45 integral with and extending from the base of thepulley 24 and the horizontal flange 46 of a fitting 48 spaced from andmovable vertically relative to said ear. The fitting 48 is mounted onsaid ear by a bolt 50 Whose base is rigidly secured to the fitting andwhose shank freely passes through an aperture in said car. A winged nut52 (hereinafter referred to as the azimuth lock) is threaded on the bolt50, accidental removal thereof being prevented by a taperpin 54 passingthrough the head of the bolt. A lug 56 integral with the fitting 48 isreceived in an aperture 58 in the ear 45 so as to maintain the flange 46in proper position beneath the flange of the ring 42. The fitting 48,bolt 50 and azimuth lock 52 are so dimensioned that when the azimuthlock is loose, the ring flange 44 can be freely turned between thefitting flange 46 and the ear 45. However, when the azimuth lock istightened, the ring flange 44 will be firmly gripped betweenthe ear 45and the fitting flange 46 thereby causing protractor dial 30 and pulley24 to rotate together.

The computing head I8 also includes an air speed vector member. Thismember comprises an arm 60 having a circular aperture 62 at one endthereof which is snugly received on the circular flange 46 of the sleeve36. Said air speed arm has an axial slot 64 in which there is disposed aslide 66 (Fig. 6) comp-rising a pin 68, a marker plate HI and a pointerblock I2, both the plate I0 and block I2 have non-circular portionsreceived in the slot 64 so that, although they may move along the arm60, they may not rotate relative thereto. Other parts of the slide 66will be later described in connection with a ground speed vector member.

The arm 60 is provided with means to enable it to be fixed relative tothe protractor dial 30. Said means may comprise a block I4 (Fig. 5)having integral lip I6 lying over the face of the protractor dial 36.The block is apertured to receive a bolt I8 whose base is fixed in theair speed arm 60 and whose other end is threaded to receive a winged nut(hereinafter referred to as the air heading lock). Bolt I8 is providedwith a taper pin 82 to prevent accidental removal of the nut 80. Theblock I4, lip I6 and nut I8 are so dimensioned that when the air headinglock is loose, the air speed arm may be freely turned about theprotractor and that when the air heading lock is tightened the air speedarm is fixed to the protractor. An index plate 84 is secured to the airspeed arm 60 and is provided with a marker 86 which in cooperation withthe protractor graduations 32 indicates the angular position of said armrelative to the protractor. The arm 60 is further provided with a linearseries of graduations 88 which indicate in miles per hour the vectordistance from the center of rotation of said arm. The marker plate I0 isprovided with a cusp 90 whose position along the graduations 88 indicatethe distance of the slide pin 68 from the center of rotation of the airspeed arm.

The computing head I8 further includes a wind speed vector member whichlike the protractor 30 and air speed arm 60 is mounted for rotationabout the center on which the pulley 24 turns. Said wind speed vectormember comprises an elongated thick plate 94 which is pinned at 95 tothe head 96 of a shaft 91 journalled in the sleeve 36. The upper'end ofthe shaft 81 has a reduced threaded portion 98 on which a nut I00 isscrewed. Said nut clamps an arm I02 to the shaft 96 for rotationtherewith. On the outer end of the arm I02 I mount a fitting I04 similarto the fitting 48. Said fitting I04 is adapted upon tightening of a nutI06 (hereinafter referred to as the wind direction lock) to clamp thearm I02 to a plate I08 firmly secured to the sleeve 36 which is fixed tothe pulley 24. When the wind direction lock I06 is loosened the arm I02may be turned by means of a knob IIO to vary the angular position of theelongated plate 94 relative to the protractor dial 30.

The bottom surface of the thick plate 94 is longitudinally slotted toreceive a plate I I2 (hereinafter referred to as the wind speed slide).Said slide is imprinted with a plurality of longitudinally spacedgraduations II4 which indicate in miles per hour the vector distance ofthe wind from the center of rotation of the wind speed slide to a pivotpin hereinafter described for the ground speed vector member.

These graduations are adapted to be read in cooperation with the forwardbeveled edge II6 of the thick plate 84. The line II8 which thesegraduations cross is adapted to be read in conjunction with the azimuthgraduations 32 on the protractor dial 30 to denote the angular positionof the wind speed slide II2 relative to said dial. To facilitate thisreading of the angular position of the wind speed slide, the bevellededge II6 may have a marker I20 imprinted thereon which is permanently inregistration with the line H8. The wind speed slide H2 is provided atits projecting end with an enlarged head I22 to facilitate manipulationof the slide. The lateral edges x I I44b'eneath the groove- I52;

offl tlie sli'debetween theshankportion and head thereof; is abruptly'steppedtmform shoulders I 24 which-"are? adapted "to" abut setba'cks'I26 in the forward edge of the plate 94 "when the. zero marking of thewind speed graduations I I4are directly 'tiveto the thick slotted/plate94;; Said means may comprise a" lever I28((hereinafter referred to 'a's'the wind speed lock) pivotally mounted on a 'piriI36secured to' theplate 94. The Wind speed lockl28'has a carnysurface I32 which isadaptedwhen saidlock is' urged in counter-clockwise direction" (asviewed fro-m Fig. 7) to be wedged against a lateral'edge of'the shankportionof the wind speed slide; A torsion spring I34 woundaround' a boltI36'secured to an ear I38 integral with the plate serves to bias thewind speed lock'l28 to wedging position.

Accidental removal of the wind speed slide II2 from theslotted'plate94is prevented by ascrew I46 fixed to theend'of'the under surface of theslide 'IIZ" adjacent a lateral edge thereof and adapted to ride in agroove I42 at the bottom of saidplate 94,

The lastmain element of the head comprises theground speed vector memberwhich includes anarm I44 having one. apertured end thereofrot'atablymounted'on the shank of.apin I 46 carriedon'the wind'speedslide I I2. The head I48 of said pin' is freceivedin a countersunk boreI50 in the arm I44 so that the bottom face of said arm may lie fiat onthe map I4. The'center of the'pin I46 is so'arranged that when the zerograduation on the wind speed slide lies imme-. diately below the bevelededge Il6', said pin will be concentric with the pulley 24; In thismanner when the wind speed slide is pulled out the readingsjthereon willbeindicative of the vector dista'nce' in miles per' hour that thecenterof the pin I46 is spaced'fromythe center of the pulley 24 and fromthe center about which the air speed arm and wind speed slide I I2rotate.

The ground speed arm I44'is provided with an axial slot I52 inwhich thedepending portion I54 (Fig; 4) ofa drift" plate I56'iss1idingly butnonrotatably accommodated. This plate I56 is apertured'to receivethe-pin 68"cf the slide 66 previously mentioned. One portion of thedrift plate is provided 'with a pointer finger I 58 in the form of-a'cusp having amarker which is adapted to bereadin conjunction withgraduations I60 on the ground speedarm to-denote'in miles per hour I thevector distance of the slide 66 from the center of the pin I462 Thelower portion of the pin 68 has -an enlarged'head I62 which rides in aslot I64 in the under surface of the ground speed arm the head I62 ofthe pin to lie flush with the bottom of the ground speedarm-I44 and thusallows this bottomsu-rface'tolie'fiat on the map-I4; Theother end of thepin 68' is threaded to receivea winged nut I66 (hereinafter referred toassthe airspeed lock) which, when tightened, will press thepointerplate16 carried by the pin 68 against the upper surface of the air speed armBOr-thereby clamping'sai'darm between said plate and the-pointer block121 This'tightening of the air :speed ,lock;1however,- will? not. clamp.the pin This slot enables Means are also providedto indicatetheangularamount of wind drift.- Said means comprises'af' plurality of' angulargraduations I10-*"im'printed on the drift plate I56 abbutthe centerofthe" pin 68. These-angular graduations are readin conjunction-with apointer I12" carried on" the block 12-. The zero mark'oftheangulargradua-- tions I16 "and the pointer*I12 are-so relativelyarranged that when' the-wind speed'slidefl I2 is set with its zeromarking below the beveled'edge I I6; the pointer I12 is registeredwiththe zero angular marking of thegraduations' I101 The foregoingconstitute all the essential structural elements ofthe computing headIII: In order to demonstrate-the use 'thereof'I'will now proceed to showhow said machine may be en1'-- ployed to solve typical problems whicharise dur- I ing the navigation of an airplane; To better ap preciatethe method employed in' working out"- these problemsyit may bementioned'that theyare calculated by the use of vectdrtriangles whosethree sides include the air speed arm 60, the wind speed slide II2,and-the ground speed arm I44, one of whose anglesinclude the driftangle, read on the drift plate I56, and'whose-three angles can bedeterminedby the winddirectiomtheair heading, and the track. When anyfour of these variables are given the remainder may be determined.

The first problem to be considered "is the-following:

Given wind speed, wind-direction; air speed. and track, to determineground speed, air heading andwind drift.-

The first operation is to set the zero of the -zero graduation on thewindspeed slide II2-be-' neath the beveled edge I I6. This will arrangethe air speedand ground speed arms Wand I44- for common rotation aboutthe center of the pulley 24 The air heading lock' is then loosenecl andthe two arms 66, I44 rotated about their common centers until theindexmark-86 is aligned with the zero azimuth graduation" 32.

The air heading lock is now locked and'the azimuth lock 52 loosened; Thecomputingheadis then moved over the map I4 and'the-groun'd speed armturned "until one of its linear beveled ruling edges I14 lies on theline indicated true north on the map rose I16 at the longitude-for"which the problem is being computed." This will" cause the zero azimuthgraduation to bear true north on themap. The azimuth-lock-52 can then betightened and left alone as'long; as any problem concerning thenavigation of the airplane is being computed at this longitude. The 651next step is to loosen the wind direction lock'106 and turn the knobIII] until the line II8 ontlie-f wind speed slide H2 is "aligned withtheazimuth' graduation 32 corresponding to the directionfrom which thewind is blowing; In Fig. 1 said knob is'set to correspond to a windblowing from 210 degrees. After the wind 'directionhas been set the winddirection lock I06 is tightened. The

operator now'loosens'the wind speed lock I28,',. pulls out the windspeed slideuntil the'speed'" graduation H4 thereon correspondingtothe'ac tual wind speed is registered with the beveled edge H6, andthen releases the wind speed lock.

The next step is to loosen the air speed lock I66 and slide the platealong the slot 64 until the pointer 90 is in registration with thegraduation 88 denoting the air speed in miles per hour. The air speedlock is then tightened and the air heading lock 80 loosened.

With the computing head l8 thus set up the ground speed arm I44 is movedover the surface of the map I4 until a ruling edge I14 lies on a mapline I18 denoting the track. A knob I19 on the free end of the arm I44facilitates manipulation thereof.

The setting of the problem is now complete and the air heading lock cannow be tightened and the computing head brought close to the observer inorder to read the solution of the problem. The ground speed will beobserved by noting the position of the pointer I58 on the scale ofground speed graduations I60. The air heading will be observed by notingthe azimuth graduation 32 with which the marker 86 is in registration,and, finally, the angle of wind drift will be observed by noting thegraduation I10 on the drift plate I56 with which the point I12 is inregistration.

Another typical problem is the following:

Given wind speed, wind direction, air speed, and air heading, todetermine ground speed and to determine and plot the tracks.

In the solution of this problem the protractor dial is set with its zeroazimuth graduation pointing north on the map and the wind speed and winddirection set into the computing head I8 as described in the firstproblem. Similarly the pointer 90 is locked at the given air speed. Thenthe marker 86 is brought into registration with the azimuth graduationfor the given air heading and there held by tightening the air headinglock 80. The computing head 18 is now moved over the surface of the mapI4 until a linear edge I14 of the ground speed arm lies passes through apoint on the map at which the airplane is known to be. A line is thendrawn on the map along said edge I14 and through said point. This linedenotes the ground track. The computing head can now be brought close tothe observer thereof who reads the ground speed and wind drift in themanner set forth in Example 1. To find the track, the observer loosensthe air heading lock 80 and the-wind speed lock I28, and pushes the windspeed slide II2 down to the zero stop. He then moves the computing headI8 and ground speed arm I44 to register a linear edge I14 with theground track. He now tightens the air heading lock and reads the azimuthgraduation registered with the mark 86. This will give the bearing ofthe track.

A third typical problem is the following:

Given wind speed, wind direction, ground speed and track, to determineair speed and air heading.

This problem is useful when two separate flight groups are to meet at anappointed spot and time. First the zero azimuth graduation is set totrue north for the given longitude and the wind speed and wind directionset into the computing head I8 as explained in the first example. Now alinear edge I14 is placed along the given route and one head used tohold the ground speed arm I44 in this position. With said arm thus heldthe slide 66 is moved along the groove I52 in the ground speed arm untilthe pointer I58 is at the given ground speed. The air speed lock I66 andair heading lock are now tightened whereupon the computing head may bebrought over to the observer and the air speed and air heading read.

It will be noted that the various elements of the computing head I8 areso arranged that the ground speed and air speed arms can be swung 360degrees relative to the wind speed slide II2. To accomplish this, thevarious locks are either disposed on different planes or at differentradii from the center of the pulley 24.

However, when theair and ground speed are relatively low and the windspeed relatively high, it will be noted that either the shank or head ofthe wind speed slide I I 2 will strike the pointer block 12 and preventa full 360 degree movement of the ground speed and air speed arms. Wherethis prevents the machine from solving a problem under any givencircumstances, I may slightly modify the construction of the slide 66 toovercome such defect. Said modified construction is shown in Fig. 8 andis generally characterized by the fact that the linear pin 68 of thefirst form of the invention is replaced by an offset pin. It will beseen, by reference to this figure, that the air speed lock I66 isthreaded on a short bolt 200. This bolt freely passes through the markerplate 10 and through a pointer plate 202, which latter, like the plate10, has a portion 204 non-rotatably and slidably received in the slot 64of the air speed arm 60. The bolt 200 is provided with a flange 206underlying the pointer plate 202 so that when the air speed lock I66 istightened the pointer plate and marker plate will clamp the air speedarm 60 between them. Below the flange 206 the bolt serves as a bearingon which one arm of an offset pin 208 is rotatably mounted. The bolt maybe peened over to permanently rotatably secure the pin. The other arm ofthe pin 208 is rotatably secured to a bolt 2I0 whose head 2l2 isslidably received in the groove I64 on the lower surface of the groundspeed arm I44. The shank of said bolt 2I0 is rotatably received in adrift plate 2I4 having a. depending portion 2 I 6 non-rotatably andslidably mounted in the slot I52 of the ground speed arm.

Said drift plate is provided with the ground speed pointer 2I8 andangular drift graduations (not shown) similar to those engraved on thedrift plate I56. The drift plate H4 and pointer plate 202 are verticallyspaced from each other a distance slightly more than the thickness ofthe wind speed slide II2 to thereby allow said slide to freely passtherebetween to a position in which it is in alignment with the groundspeed arm 60. It will be seen that by swinging the offset pin 208 to theright or left the wind direction may be set at or as close as desired tothe airplane heading.

It will thus be seen that there is provided a device and method forusing the same which achieves the several objects of this invention andwhich is well adapted to meet the conditions of practical use.

As various possible embodiments might be made of the above invention,and as various interconnected longitudinally slotted arms, a connectingmechanism for pivotally and slidably interconnecting said armscomprising a pivot screw slidably mounted in one of asid slots andextending through the other of said slots, at pointer member encirclingsaid screw and positioned between said arms, said pointer member havingformed thereon a key portion received in the slot in one of said membersto hold said pointer against pivotal movement relative thereto, a secondpointer member encircling said screw above the other of said arms, saidsecond pointer membernincluding a key portion received in the slot inthe other of said arms to hold said second pointer against pivotalmovement relative to. said other arm, and a clamping nut threaded uponsaid screw and bearing against said second pointer member for lockingsaid pivot screw against sliding movement relative to one of said arms.

2. In a plotting instrument including a pair of interconnected slottedarms, a connection mechanism for slidably and pivotally interconnectingsaid arms comprising a pivot screw slidably received within the slot inone of said arms,

a protractor scale surrounding said screw and positioned between saidarms, said protractor scale including a key portion received in the slotin the lower one of said arms to hold said protractor scale againstpivotal movement relative thereto, a pointer member encircling saidpivot screw and disposed between said arms, said pointer memberincluding a key portion received in the slot in the upper one of saidarms to hold said pointer against pivotal movement relative to the upperone of said arms, whereby the position of said pointer on saidprotractor scale indicates the angular disposition of said arms relativeto each other, and clamping means coacting with said pivot screw forlocking said pivot screw against sliding movement relative to one ofsaid 20 arms.

ALLEN H. KENT.

